My research is in quantum information and its interplay with mathematics, computer science, and theoretical physics. Motivated by quantum information, I study mathematical problems in optimization, representation theory, and invariant theory through the lens of computation. I am supported in part by an NWO Veni grant on Quantum bits in space and time and by an NWO KLEIN grant on Taming tensors: an optimization approach to computational invariant theory. I am part of the NWA quantum/nano route and a member of the Geometry and Quantum Theory and DIAMANT mathematical research clusters.
Curriculum vitae: [pdf]
We are setting up a new specialization “Discrete Mathematics and Quantum Information” in the MSc Mathematics (starting in fall 2021).
I am very honored to receive an Early Career Award by the Royal Netherlands Academy of Arts and Sciences (KNAW).
I will be giving lectures at TASI 2021 in June.
Together with Jay Armas, I organized a focus session on Information at all length scales: from black holes to quantum information and living systems at Physics@Veldhoven.
In Spring 2021 we will offer another edition of our MasterMath course Quantum Information Theory.
My grant proposal “Taming tensors: An optimization approach to computational invariant theory” was selected for funding by the NWO. Yay!
We organized a reading group “From Euclidean to Geodesic Convex Optimization”.
We organized a Lorentz Center workshop on “Complexity from Quantum Information to Black Holes” from June 2-5
I gave a lecture series on Quantum Information at the 14th Kavli Asian Winter School on Strings, Particles and Cosmology at Tohoku University in Jan 2020. Slides available here.
Together with Peter Bürgisser, I organized a mini-symposium on “Efficient algorithms for geometric invariant theory” at SIAM-AG 2019. See here for details.
Together with Ankit Garg, Rafael Oliveira, and Avi Wigderson, I organized a workshop on scaling algorithms and applications at FOCS 2018. See here for details.
New article published in Communications of Mathematical Physics
- Valerie Bettaque (MSc project)
- Tomas Bosschieter (BSc project)
- Jonas Helsen (postdoctoral researcher)
- Friso Lohmann (BSc project)
- Harold Nieuwboer (PhD candidate), classical & quantum optimization algorithms
- Ricardo Rivera (MSc project)
- Freek Witteveen (PhD candidate), quantum information & field theory
- Yinan Li (2018-20, postdoc; now designated assistant professor at Nagoya)
- Marten Folkertsma (2019-20, MSc project; now PhD student at CWI)
- Laurens Ligthard (2019-20, MSc project on quantum entropy; now PhD student at Köln)
- Maxim van den Berg (2020, BSc project on lossless audio compression)
- Slawi Dimitrov (2020, BSc project on randomized benchmarking)
- Emma Loos (2018-19, MSc project on cMERA and holography; now PhD student at Würzburg)
- Jeroen Dekker (2018-19, MSc project on holographic tensor networks and smooth entropies)
- Lars van Geest (2019, BSc project on tensor networks for the Motzkin spin chain)
- John Paul Marceaux (2019, academic skills project on design theory)
- Philip Verduyn Lunel (2018-19, MSc project on quantum simulations and many-body localization)
- Raja Damanik (2018, MSc project on optimality in stabilizer testing; now PhD student at Sydney)
- Casper Guyrik (2018, MSc project on quantum algorithms for factoring and post-quantum RSA, daily supervised by Ronald de Wolf; now PhD student at Leiden)
- Philip Roeleveld (2018, BSc project on a truncated tensor scaling algorithm)
- Wouter Borg (2018, BSc project on entanglement in the stabilizer formalism)
Next group meeting: See Slack.
Publications and Preprints
Fall 2021: Bachelor’s course Introduction to Information Theory [more]
Fall 2021: Master Seminar in Discrete Mathematics and Quantum Information
(a new specialization!)
Fall 2021: Master Seminar Theoretical Physics
Fall 2021: Web class Quantum Quest [more]
Spring 2021: MasterMath course Quantum Information Theory [more]
Fall 2020: Bachelor’s course Introduction to Information Theory [more]
Fall 2020: Master Seminar Theoretical Physics [more]
Fall 2020: Reading group From Euclidean to Geodesic Convex Optimization [more]
Fall 2020: Web class Quantum Quest [more]
Spring 2020: MasterMath course Quantum Information Theory [more]
Spring 2020: Master Seminar in Algebra, Geometry and Mathematical Physics
Spring 2020: Reading group From Euclidean to Geodesic Convex Optimization [more]
Fall 2019: New Bachelor’s course Introduction to Information Theory [more]
Fall 2019: Master Seminar in Algebra, Geometry and Mathematical Physics [more]
We read Bernd Sturmfels’ book “Algorithms in Invariant Theory”.
Fall 2019: Master Seminar Theoretical Physics [more]
Spring 2019: New MasterMath course Quantum Information Theory [more]
Spring 2019: Master Seminar in Algebra, Geometry and Mathematical Physics [more]
We read Sagan’s book “The Symmetric Group”. Here is a refresher on basic representation theory roughly following Sections 1.1–1.6.
Fall 2018: Web class Quantum Quest [more]
Spring 2018: New Master course on Symmetry and Quantum Information [more]
I previously taught a similar course at Stanford University. Watch this lecture as a teaser. I also taught an abridged version of this course at IES in Cargese.
See here for introductory lectures on quantum information, field theory, and gravity (with an emphasis on links between these fields).
Quantum Software and Society
- Nature Insight
- Quantum software manifesto
- Ronald de Wolf’s essay on the impact of quantum computing on society
- John Preskill’s essay on noisy intermediate-scale quantum technology
- Gate-level quantum software platforms overview as of July 2018
- “Quantum Brascamp-Lieb inequalities”, IPAM 2021 [video] [pdf]
- “Maximum likelihood estimation for tensor normal models”, Firenze 2021
- “Fun with Replicas & Holographic Tensor Networks”, Perimeter 2020 [video]
- “Tensors, invariants, and optimization”, Leipzig 2019, Berkeley 2019, Berlin 2020, Chennai 2020, Perimeter 2020 [pdf] [pdf] [pdf] [pdf] [pdf]
- “Quantum circuits for the Dirac field in 1+1 dimensions”, AEI 2019, Stanford 2019, YITP 2019 [pdf] [video] [pdf] [pdf]
- “Quantum marginals, invariants, and non-commutative optimization”, Leiden 2019, SIAM-AG 2019 [pdf] [pdf]
- “Quantum Marginals, Entanglement, and Symmetries”, DPG 2019 [pdf]
- “An invitation to tensor networks”, IAS 2018 [video]
- “Quantum Information and Holography”, DESY 2018 [pdf] [video]
- “Schur-Weyl Duality for the Clifford Group: Property testing, de Finetti representations, and a robust Hudson theorem”, QIP 2018, Boulder 2018, Bad Honnef 2018 [pdf] [video] [pdf] [pdf]
- “Quantum entanglement and space-time”, Groningen 2018 [html] [video]
- “Convexity, marginals, and moment polytopes”, IAS 2018 [pdf] [video]
- “Introduction to Quantum Programming”, QuSoft 2018
- “Quantum marginal problem, tensor scaling, and invariant theory”, NMC 2018 [pdf]
- “Rigorous entanglement renormalization from wavelets”, KITP 2017, Caltech 2017, AEI 2018, Amsterdam 2018, GGI 2018 [pdf] [video] [pdf] [pdf] [pdf]
- “When is a quantum state a stabilizer state?”, QuSoft 2017, QuTech 2018 [pdf]
- “Bulk reconstruction, error correction, and recovery maps”, KITP 2017 [video]
- “Tensor network models of holography”, DESY 2017
- “When is a state a stabilizer state? Testing stabilizer states with six copies”, CWI 2017
- “Tensors and Quantum Physics”, Auburn 2017 [video]
- “Multiparty entanglement, random codes, and quantum gravity”, Coogee 2017 [pdf], “Multipartite entanglement in toy models of holography”, Simons Center for Geometry & Physics 2016 [pdf] [video]
- “Entanglement in random tensor networks”, Georgia Tech 2016 [pdf]
- “Holographic duality from random tensor networks”, MIT 2015, KITP 2016, Cologne 2016, IQC 2016 [pdf] [pdf] [video] [other]
- “Moment polytopes & computational complexity”, Berkeley 2015 [pdf]
- “The Holographic Entropy Cone”, ETHZ, Caltech, CRM 2015; QIP 2016 [pdf short] [video] [pdf long]
- “Kronecker coefficients and complexity theory”, Dartmouth 2015, Rome 2016 [pdf]
- “Topologically ordered models in higher dimensions”, QGQIT 2015 [pdf]
- “Random Quantum Marginals”, IAS 2014 [video]
- “A Heisenberg Limit for Quantum Region Estimation”, ISIT 2014 [pdf]
- “The Quantum Marginal Problem”, DPG Spring Meeting 2014 [pdf]
- “Entanglement Polytopes”, QIP 2013; QSIT Lunch Seminar [pdf] [video] [science] [pdf] [explorer]
- “Quantum Entropies and Representation Theory”, IHES 2013 [pdf]
- “Computing Multiplicities of Lie Group Representations”, FOCS 2012 [pdf] [video]
- “Quantum State Tomography of 1000 Bosons”, SPS Meeting 2012 [pdf]
- “Quantum Marginals and Classical Moments”, IMS 2013 [pdf]
- “Eigenvalue Distributions of Reduced Density Matrices”, ICMP 2012 [pdf]
- Solve the quantum marginal problem and compute entanglement polytopes using our new tensor scaling algorithm.
- Use wavelets to approximate ground states of free fermion theories.
- Prove new holographic entropy inequalities using the contractor
- Just a moment! – an algorithm for computing moment cones for the quantum marginal problem
- Explore entanglement polytopes
- Compute Kronecker coefficients using barvikron (Python) or the new Kronecker Maple package
- Download the quantum sandbox for Octave/Matlab